Sketching contours maths?

Hi, im very new to this so not sure if this is the correct section

I have to sketch a contour for, z^2=9-4x^2-4y^2
So lets make z^2=c
then after some rearranging you get
x^2+y^2=(9-c)/4
its a circle. But im not sure what the radius is. Is it root (9-c)/4? or is it left as it is. Im asking since i made z^2=c and not z=c. Am i doing it right? please help. Many thanks